University of Alberta

Radio Frequency Characterization and Modelling of Low Temperature Co-

Fired Ceramic (LTCC) Material and Devices

by

Fatemeh Kalantari

A thesis submitted to the Faculty of Graduate Studies and Research

in partial fulfillment of the requirements for the degree of

Master of Science

in

Integrated Circuits and Systems

Department of Electrical and Computer Engineering

©Fatemeh Kalantari

Spring 2014

Edmonton, Alberta

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To my beloved family.

Abstract

The focus of this dissertation is on the characterization of Low Temperature Co-

fired Ceramic (LTCC) for microwave and Radio Frequency (RF) applications.

The LTCC substrates’ excellent microwave properties make them great

candidates for the packaging of RF devices, as well as the fabrication of passive

RF and microwave components. In order to utilize LTCC, the first step is to

characterize its microwave properties including the dielectric constant and loss

tangent which will enable designers to design and simulate the RF behavior of

LTCC components accurately. Investigating various measurement techniques, we

decided to use a parallel plate capacitor for the characterization of a LTCC

substrate from 100 MHz to 1 GHz and a conductor backed coplanar waveguide

from 1 GHz to 10 GHz. After fabrication of several test structures on Dupont 951

LTCC substrates, the scattering parameters were measured using a 110 GHz

Vector Network Analyzer and the effect of the pads were de-embedded from

measurement results. Through this process, we developed a novel fast de-

embedding method which de-embeds the effect of the pads and parts of the

transmission lines as opposed to the conventional method, where only the effect

of the pads is removed. This will result in a similar electromagnetic field around

the de-embedded structure to that of a test structure where no pad exists.

Therefore, the proposed de-embedding method produces more accurate loss

tangent and dielectric constant results compared to the conventional method.

Acknowledgements

I owe my profound gratitude to my supervisor Dr. Kambiz Moez whose

encouragement, support and valuable advice has led me to go through this

program and to make this work a success. It has been a great privilege to be a part

of his research team.

I would like to express my grateful thanks to Mr. Kevin Yallup, CTO of Alberta

Centre for Advanced MNT Products (ACAMP), our project partner, for defining

this project and the engaging assistance from the University of Alberta and

providing us with their Dupont 951 LTCC products.

I am grateful to my colleagues and lab mates in Electrical and Computer program

for their help and support in various aspects of my research.

Finally, I would like to express my appreciation to my husband and my family for

their caring and supportive attitude in all aspects of my life.

Contents Introduction ...................................................................................................................................... 1

1.1 Motivation ....................................................................................................................... 1

1.2 Outline of Thesis ............................................................................................................. 3

Background ...................................................................................................................................... 6

2.1 Dielectric Constant and Loss Tangent ............................................................................ 6

2.2 Substrate Material Measurement Techniques ................................................................. 8

2.2.1 Coaxial Probe ............................................................................................................. 8

2.2.2 Transmission line........................................................................................................ 9

2.2.3 Free Space ................................................................................................................ 10

2.2.4 Resonant Cavity........................................................................................................ 10

2.2.5 Parallel Plate Capacitor ............................................................................................ 11

2.2.6 Comparison of Characterization Methods ................................................................ 12

2.3 ACAMP Design Parameters ......................................................................................... 13

2.4 Transmission lines ........................................................................................................ 17

2.4.1 CBCPW .................................................................................................................... 18

2.4.2 Stripline .................................................................................................................... 20

2.4.3 Microstrip ................................................................................................................. 21

2.5 Measurement ................................................................................................................. 23

2.5.1 Scattering Parameters ............................................................................................... 23

2.5.2 The Vector Network Analyzer (VNA) ..................................................................... 24

LTCC Dielectric Characterization .................................................................................................. 26

3.1 Introduction ................................................................................................................... 26

3.2 Low Frequency Characterization (100 MHz to 1 GHz) ................................................ 27

3.3 High Frequency Characterization (1GHz to 10 GHz) ................................................... 30

3.3.1 CBCPW Electromagnetics Simulation ..................................................................... 33

3.3.2 Stripline Electromagnetics Simulation ..................................................................... 34

3.3.3 Microstrip Electromagnetics Simulation .................................................................. 35

3.4 Dielectric Constant and Loss Tangent Calculations ..................................................... 38

3.4.1 Dielectric Constant ................................................................................................... 38

3.4.2 Loss Tangent ............................................................................................................ 40

3.5 Measurement ................................................................................................................. 41

3.5.1 Measurement versus Simulation ............................................................................... 42

3.6 De-embedding DUT .................................................................................................... 51

3.6.1 Modeling Port as a RLC Network ............................................................................ 52

3.6.2 Simulation Results .................................................................................................... 54

3.7 Summary ....................................................................................................................... 58

Proposed De-Embedding Method .................................................................................................. 60

4.1 Introduction ................................................................................................................... 61

4.2 Theory of Proposed De-embedding Method ................................................................ 63

4.3 Electromagnetic Field Comparison ............................................................................... 64

4.4 Characterization of Test Fixtures .................................................................................. 67

4.5 Dielectric Characterization Results ............................................................................... 71

4.6 Modeling of Other LTCC Devices................................................................................ 73

4.7 Summary ....................................................................................................................... 75

Conclusions .................................................................................................................................... 76

List of Tables

Table 2.1 Dupont 951 tape material physical and electrical properties [22]. ................................ 13 Table 2.2 Dupont 951 tape material thermal and mechanical properties [22]. .............................. 14 Table 2.3 Dupont 951 tape design parameters and considerations [23]. ....................................... 14 Table 2.4 Dupont 951 tape design parameters and considerations for passive devices. ................ 15 Table 3.1 Design Guidelines for LTCC according to Hirai [41]. ................................................... 29 Table 3.2 Design parameters of the CPWs, microstrips and striplines. .......................................... 31 Table 3.3 Design parameters of CBCPW with ground plane. ........................................................ 37 Table 3.4 Loss tangent and dielectric constant of LTCC. .............................................................. 58 Table 4.1 Improved loss tangent of Dupont 951 LTCC. ................................................................ 72

List of Figures Figure 1.1. Four layer LTCC substrate with integrated passives, buried capacitors, inductors and

resistors, from Dupont the miracles of science [8]. .......................................................................... 3 Figure 2.1. Coaxial probe method to characterize a substrate. ......................................................... 8 Figure 2.2. Transmission line method; waveguide and coaxial line case. ........................................ 9 Figure 2.3. Free space measurement method. ................................................................................ 10 Figure 2.4. Resonant cavity measurement method. ....................................................................... 11 Figure 2.5. Parallel plate measurement method. ............................................................................ 12 Figure 2.6. Spiral inductor with gold on Tape 951 from Dupont [24]. ........................................... 16 Figure 2.7. Dual port and single port, multi finger and single capacitors with gold on Tape 951

from Dupont [25]. .......................................................................................................................... 16 Figure 2.8. Resistors on Tape 951 from Dupont [26]. .................................................................... 17 Figure 2.9. Coplanar Waveguides (CPW) with no lower ground plane. ........................................ 18 Figure 2.10. Conductor-Backed Coplanar Waveguides (CBCPW) with lower ground plane. ....... 18 Figure 2.11. Symmetric (balanced) stripline, case TD1 = TD2. ........................................................ 20 Figure 2.12. Microstrip transmission line. ...................................................................................... 22 Figure 2.13. DUT transmitted, incident and reflected signals. ....................................................... 23 Figure 3.1. Ideal parallel plate capacitor, A is the area of the plates, and d is the plate separation. 28 Figure 3.2. Three dimensional visualization of our designed capacitors in Agilent Advanced

Design System. ............................................................................................................................... 30 Figure 3.3. Scattering parameters of a capacitor with A=7*7 mm^2, and d=100 um, “κ” =7.99, T=6

um, σ=6.3*e+07 S/m. ..................................................................................................................... 30 Figure 3.4. Layouts of test structures including the transmission lines and capacitors. ................. 32 Figure 3.5. Designed 50 ohm sample CBCPW with W=246 µm, l=10150 µm, G=100 µm, we have

considered the Dupont 951 technology: T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99. 33 Figure 3.6. Scattering parameters and smith chart of CBCPW. ..................................................... 34 Figure 3.7. Designed 50 ohm sample stripline with W=151 µm, l=10150 µm, we have considered

the supplier technology: T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99. ........................ 34 Figure 3.8. Scattering parameters of stripline. ................................................................................ 35 Figure 3.9. Designed 50 ohm sample microstrip with W=761 µm, l=1150 µm, we have considered

the supplier technology: T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99. ........................ 35 Figure 3.10. Scattering parameters and smith chart of microstrip. ................................................. 36 Figure 3.11. VNA probe station at M2M. ...................................................................................... 41 Figure 3.12. Test structures fabricated by ACAMP on Dupont 951 LTCC. ................................. 42 Figure 3.13. 50 ohm miniature Z probe pitch of the VNA. ........................................................... 43 Figure 3.14. Input port of a stripline to be measured under VNA’s microscope. ........................... 43 Figure 3.15. ADS file to compare measurement results and Electromagnetic simulation data. ..... 44 Figure 3.16. Measured and simulated scattering parameters of the 650 µm CBCPW. .................. 45 Figure 3.17. Measured and simulated ΔΦS21 of the 650 µm CBCPW. ........................................... 45 Figure 3.18. Measured and simulated S21 magnitude of the 650 µm CBCPW. .............................. 46 Figure 3.19. Measured and simulated scattering parameters of the 1150 µm CBCPW. ................ 46 Figure 3.20. Measured and simulated ΔΦS21 of the 1150 µm CBCPW. ........................................ 47 Figure 3.21. Measured and simulated S21 magnitude of the 1150 µm CBCPW. ............................ 47 Figure 3.22. Measured and simulated scattering parameters of the 5150 µm CBCPW. ................ 48 Figure 3.23. Measured and simulated ΔΦS21 of the 5150 µm CBCPW. ......................................... 48 Figure 3.24. Measured and simulated ΔΦS21 of the 5150 µm CBCPW. ......................................... 49 Figure 3.25. Measured and simulated scattering parameters of the 10150 µm CBCPW................ 49

Figure 3.26. Measured and simulated ΔΦS21 of the 10150 µm CBCPW. ...................................... 50 Figure 3.27. Measured and simulated S21 magnitude of the 10150 µm CBCPW. .......................... 50 Figure 3.28. Signal flow graph representing the test fixture halves and the Device Under Test

(DUT) [44]. .................................................................................................................................... 51 Figure 3.29. Measured real part of the port impedance. ................................................................. 53 Figure 3.30. RLC model for the transmission line’s ports [46]. .................................................... 53 Figure 3.31. Dielectric constant of the LTCC using the ADS simulation results up to 40 GHz. ... 55 Figure 3.32. Dielectric constant of the LTCC using the measurement results before de-embedding

up to 10 GHz. ................................................................................................................................. 56 Figure 3.33. Loss tangent of the LTCC using the measurement results before de-embedding up to

10 GHz. .......................................................................................................................................... 56 Figure 3.34. Dielectric constant of the LTCC using the measurement results after de-embedding

up to 10 GHz. ................................................................................................................................. 57 Figure 3.35. Loss tangent of the LTCC using the measurement results after de-embedding up to 10

GHz. ............................................................................................................................................... 57 Figure 4.1. Conventionally de-embedded transmition line in the middle and the proposed de-

embedded line at the bottom. ......................................................................................................... 62 Figure 4.2. 5150 µm CPW transmission line including input and output ports, W=246 µm, l=5150

µm, G=100 µm, T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99. ..................................... 63 Figure 4.3. CPW Electric-E and Magnetic-H field distribution. .................................................... 65 Figure 4.4. (a) Electric field distribution of 10150 CBCPW, (b) Magnetic field distribution of

10150 CBCPW. .............................................................................................................................. 67 Figure 4.5. (a) Electric field distribution of 10150 CBCPW, (b) Magnetic field distribution of

10150 CBCPW.. ............................................................................................................................. 72

Figure 4.6. Loss tangent of Dupont 951 LTCC using measurement results after de-embedding up

to 10 GHz using our proposed analytical method ………………………………………………..72

Figure 4.7. Model of stripline in ADS assuming Dupont 951 LTCC as its substrate. .................... 73 Figure 4.8. Creation of the substrate of Dupont 951 LTCC for a stripline in ADS. ....................... 74

List of Symbols

W: Width of signal conductor in a transmission line.

S: Spacing between conductor and ground planes.

H: Thickness of substrate.

t: Thickness of signal conductor.

: Relative dielectric constant.

: Dielectric constant.

Z0: Characteristic impedance.

: Effective dielectric constant.

K (k): complete elliptic integral of the first kind

S11: Input reflection coefficient of DUT.

S21: Forward transmisssion coefficient of DUT.

S22: Output reflection coefficient of DUT.

S12: Reverse transmission coefficient of DUT.

κ: Dielectric constant of the material.

ε0: 8.85 x 10-12 F/m is the free space permittivity.

A: Area of the plates.

d: Plate separation.

σ: 6.3*e+07 S/m is the electrical conductivity.

L: transmission line length.

α: Attenuation constant in decibel per centimeter.

β: the phase constant in cm-1.

ΔΦS2: the phase shift of transmission coefficient S21.

R: Resistance.

L: Inductance.

C: Capacitance.

G: Conductance.

: Loss tangent.

Acronyms

LTCC Low Temperature Co fired Ceramic

HTCC High Temperature Co fired Ceramic

CBCPW Conductor-Backed Coplanar Waveguides

CPW Coplanar Waveguides

VNA Voltage Network Analyzer

DUT Device Under Test

MUT Material Under Test

ACAMP Alberta Centre for Advanced MNT Products

RF Radio Frequency

RFIC Radio Frequency Integrated Circuits

CAD Computer Aided Device

ADS Advanced Design System

EM Electro-Magnetic

MEMS Micro Electromechanical Systems

MMIC Monolithic Microwave Integrated Circuits

MIC Microwave Integrated Circuits

GSG Ground Signal Ground

MATLAB Matrix Laboratory

1

Chapter 1

Introduction

1.1 Motivation

The continuing growth in wireless communication demands the development of

low-cost RF/microwave components, which are required for the operation of

wireless systems [1]. While semiconductor technologies such as Complementary

Metal Oxide Semiconductor (CMOS) are extensively used for integrating all of

the components of wireless transceivers onto a single chip, the packaging of these

integrated circuits and their connections to off-chip components remains a

challenge when developing fully integrated wireless systems [2, 3]. As a result,

there is strong demand for the development of packaging technologies that offer

excellent microwave properties and great compatibilities with advanced

semiconductor processes.

While the majority of wireless devices and systems use conventional printed

circuit boards, it is becoming obvious that this kind of technology does not cover

the microwave and RF performance needs of a circuit for the commercial or

technical field [4]. Recently, Low Temperature Co-fired Ceramic (LTCC), which

was originally developed for the application in high temperature electronic

packaging, has been considered as an excellent candidate for RF/microwave

2

applications [5]. LTCC technology is a multi-layer ceramic with an excellent

combination of properties for high frequency applications where stable and

uniform properties are required over a wide frequency range. LTCC’s three

dimensional structures that have buried, native passive components offers a

higher circuit density than organic laminate technologies [6].The new gold and

silver conductor system, DuPont Green Tape™ LTCC material, was developed

for high frequency applications up to 100GHz where low loss characteristics are

desired [5,6].

Green (Unfired) Dupont tape is provided in different sheet sizes and thicknesses,

it is cast on polyester backing suitable for processing along with the individual

layers. The process flow consists of preconditioning in a nitrogen dry box for 24

hours. Then, in each tape layer, vias for the electrical connections are formed

using mechanical punching or laser drilling. Next, the conductors are created

using a traditional thick film screen printer [7]. Co-firing and post-firing processes

are the procedures which would be applied to the resistors, dielectrics and

conductors. At the end of the fabrication process, the final inspection is done on

all of the laminate samples according to an applicable standard; a detailed process

flow of Dupont 951 is described in [8, 9].

Accurate designing at radio frequencies requires precise knowledge of the

substrate material’s characteristics such as the dielectric constant and loss tangent,

to enable circuit designers to predict the RF/microwave properties of the LTCC

packages and components [10].

3

There has been a variety of measurement techniques to characterize the dielectric

properties of a material based on different factors such as: the frequency range,

the material properties, the temperature and the cost. For instance, using a coaxial

probe is best for lossy Material under Test (MUT) that are liquid or semi-solids

since it is a broadband, convenient, non-destructive method. While for high

temperature, large flat samples, it is more convenient to apply a non-contacting

free space measurement to find the permittivity and permeability of the material.

For small, low loss MUT samples, using a resonant cavity would fit best, and for

an accurate measurement at low frequency of thin flat sheets, using a parallel

plate capacitor is suggested [11, 12].

Figure 1.1. Four layer LTCC substrate with integrated passives, buried capacitors, inductors and

resistors, from Dupont the miracles of science [8].

1.2 Outline of Thesis

Chapter 2 of this dissertation will briefly review the theoretical background

required throughout the thesis. Physical and electrical properties of the Dupont

951 tape material that is provided by our project partner, ACAMP, will be

4

presented, in addition to the design parameters, and the passive and active

devices’ design rules. The various measurement techniques required for substrate

characterization will be discussed to figure out a specific practical technique to

find the dielectric constant and loss tangent of the Dupont 951 LTCC material

from 100MHz to 10 GHz. Some important configurations of the transmission

lines such as the Conductor- Backed Co Planar Waveguide (CBCPW), microstrip

and striplines will be discussed, and their applications briefly introduced. A brief

overview of the scattering parameters and a measurement technique using the

Agilent vector network analyzer will be presented.

Chapter 3 reviews the dielectric characterization methods. Based on this

investigation, we will conclude that the best technique to characterize the LTCC

for the low frequency range is to design parallel plate capacitors, because of the

parallel-plate capacitors’ low resonance frequency. For the characterization of the

LTCC at higher frequencies, we choose CBCPWs for their unique characteristics

at high frequencies. Using Agilent App-CAD and ADS software, we design a set

of CBCPWs with different dimensions. In order to verify the models, we utilize

the ADS EM simulations to ensure the proper operation of the test structures in

the required frequency range. The next step will be calculating the dielectric

constant and loss tangent based on the “Conformal Mapping Technique” in which

the measured scattering parameters are used to estimate the dielectric constant of

the material. After the models are fabricated on Dupont 951 substrate, a 110 GHz

VNA with its 50 ohm probe station will be used to measure the scattering

parameters of the fabricated test structures. To obtain the scattering parameters of

5

the CBCPW test structures, the effects of the pads are de-embedded from the

measured scattering parameters using a conventional de-embedding method.

Finally, the dielectric constant is calculated using the “Conformal Mapping

Technique”.

In Chapter 4, we will propose an accurate analytical method for de-embedding

the transmission lines which will result in a more accurate estimation of the

dielectric properties of the material. In this method, instead of only de-embedding

the pads, we de-embed the pads and parts of the connecting transmision lines to

obtain an electromagnetic enviroment similar to that of a test structure without

pads. As a result, the proposed method produces more accurate results compared

to the conventional de-emebdding method.

Finally, the thesis will be concluded in Chapter 5 by summarizing the

contributions of this work.

6

Chapter 2

Background

In this chapter, we will first have a brief description of the materials’ dielectric

constant and loss tangent. Then there will be a description of the various

measurement techniques to characterize the dielectric properties of the LTCC

material. Once that is established, the Dupont 951 tape material’s physical and

electrical properties provided by ACAMP will be presented in addition to the

design parameters, and the passive and active devices’ design rules. Some

important transmission line structures such as the CBCPWs, microstrips and

striplines will be discussed as well as a brief introduction to their applications in

sections 2.4.1 through 2.4.3. Finally, we will briefly review the measuring of the

scattering parameters using vector network analyzers in section 2.5.

2.1 Dielectric Constant and Loss Tangent

The dielectric constant ( is the ratio of the permittivity of a substance

( ) to the permittivity of free space ( . It defines the extent to which a

material concentrates electric flux, in other words, it is the electrical equivalent of

relative magnetic permeability,

7

The dielectric constant and the effective dielectric constant are two different

variables. The dielectric constant is a bulk material property; the effective

dielectric constant is a parameter that depends on the transmission line geometry.

Permittivity is actually a complex number that is an "epsilon" which is made up of

two parts,

Microwave engineers usually deal with the ratio between the two, which is called

the tangent delta,

If the tangent delta is zero, there is no loss due to the dielectric; for example, dry

air has no dielectric loss.

In fact, the loss tangent is a parameter of a dielectric which quantifies its inherent

dissipation of electromagnetic energy and is proportional to the frequency. The

term refers to the tangent of the angle in a complex plane between the resistive

component of an electromagnetic field and its reactive component [13].

8

2.2 Substrate Material Measurement Techniques

There has been a variety of measurement techniques developed to characterize a

substrate material based on different factors such as: frequency range, material

properties, temperature, cost and some other factors which will be described in

this section [14].

2.2.1 Coaxial Probe

By immersing the open ended coaxial probe into a liquid, the material’s properties

are measured. If the material is solid or a powder, the probe touches it to a flat

face.

The electromagnetic field at the probe end fringes into the material and changes

as it makes contact with the MUT, then the forward transmission coefficient, S11,

is measured and the dielectric constant is calculated. In this method, the

measuring system includes an impedance analyzer and software [15].

.

Figure 2.1. Coaxial probe method to characterize a substrate.

9

To specify the features of this method, we can mention its suitability for

broadband application, and simplicity. It is a good measurement method for liquid

and semi-solid materials with semi-infinite thickness that are non-magnetic and

isotropic. In this technique we have a limited dielectric constant and a loss tangent

with limited accuracy and resolution [15].

2.2.2 Transmission line

In this method, the material is placed inside a portion of an enclosed transmission

line which is a rectangular waveguide or coaxial line as shown in Figure 2.2.

Using vector network analyzer software such as 85071E and an external

computer, the measured reflected and transmitted signals are converted to

material properties including the dielectric constant and loss tangent [16].

The coaxial transmission line is difficult to manufacture but covers a wide range

of frequencies, while a rectangular wave guide is simpler to machine but their

frequency coverage is banded.

The features for a material under testing are: having no air gaps at the fixture

walls, being smooth, having flat faces, being perpendicular to the long axis, and

being homogeneous. This is a broad band method in which the low frequency is

limited by the practical sample length, and depending on the sample length its low

Figure 2.2. Transmission line method; waveguide and coaxial line case.

10

loss resolution is limited. This method is capable of measuring magnetic and

anisotropic materials [17].

2.2.3 Free Space

This method takes advantage of using some antennas to focus the microwave

energy through a material without a need for a test fixture as shown in Figure 2.3.

This method is applicable to high temperature materials in hostile environments,

since it is a non-contacting method. The measuring system includes a vector

network analyzer software such as 85071 and a computer.

Material assumptions are: large, flat, homogeneous, and parallel-faced samples.

This method is a non-contacting non-destructive one for high temperature samples

which can measure magnetic materials as well. It is a high frequency method with

a low end limited by the practical sample size, in which the antenna polarization

may vary with anisotropic materials [18].

2.2.4 Resonant Cavity

This is a resonant technique versus the broadband techniques talked about

previously. Resonant cavities are structures with high quality factors that resonate

at certain frequencies, in which a piece of sample material affects their quality

factor and centre frequency. The complex permitivity , is then calculated from

Figure 2.3. Free space measurement method.

11

these parameters at a single frequency using a network analyzer software and an

external computer. The most widely purterbation cavity method as described in

[19] uses a rectangular wave guide with iris-coupled end plates which operates in

the TE10n mode, as shown in Figure 2.4. To measure the dielectric constant, the

sample is inserted in the middle of a wave guide length, then an odd number of

half wavelengths will cause a maximum electric field which can lead to a

dielectric constant measurement.

Figure 2.4. Resonant cavity measurement method.

Resonant techniques are practical in high impedance environments, but only at

one or a few frequencies. These measurements are well suited for small samples

and low loss materials. While broad band techniques require low impedance

environments and the measurement can be done at any frequency, they need

larger samples to obtain reasonable measurements.

2.2.5 Parallel Plate Capacitor

In this method, a thin sheet of material is inserted between two electrodes to form

a capacitor. The measuring system consists of an impedance analyzer and a

fixture. More information on the low frequency materials’ measurement solutions

is available in the application notes [20, 21].

12

2.2.6 Comparison of Characterization Methods

Many factors are important in selecting the most appropriate measurement

technique such as: the frequency range, the required measurement accuracy, the

material properties and form, the sample size restrictions, whether it needs to be

destructive or non-destructive, contacting or non-contacting, the temperature and

the cost. Since our concern is to work in a wide frequency range, the resonant

cavity methods would be useless because resonant techniques are practical at one

or a few frequencies. The free space measuement technique is applicable to high

temperature materials in hostile environments, but we have our measurements at

room temperature. Coaxial probe technique is a good measurement method for

liquid and semi-solid materials with semi-infinite thickness; however our concern

is to measure the dielectric properties of a solid and very thin substrate. Other

than that, coaxial probe method offers a limited dielectric constant and a loss

tangent with limited accuracy and resolution. Thus taking advantage of the

transmission line method would be the best decision since the features for a

material under test mentioned in Section 2.2.2 is completely compatible to

Dupont 951 substrate. In this method, the material is placed inside a portion of

enclosed CBCPWs which are accurately measurable using our in-house vector

Figure 2.5. Parallel plate measurement method.

13

network analyzer. Besides, the transmission line method is a broad band

technique and would be appropriate for our frequency range of 1GHz to 10 GHz.

However, for frequencies from 100 MHz to 1 GHz using the parallel plate

capacitor seems to be more appropriate since this is a simple, accurate method for

low frequencies and works properly for thin, flat sheet samples such as our six

layer 600 µm LTCC.

2.3 ACAMP Design Parameters

Dupont 951 tape material’s physical and electrical properties are provided in

Table 2.1.

Table 2.1. Dupont 951 tape material physical and electrical properties [22].

Dupont 951

Tape

Physical and electrical

properties

Substrate thickness 50,114,165,254

Substrate size 150 mm * 150 mm

Dielectric constant 7.8 at 1MHz

Insulation resistance 1*10^12 ohm

Fired effective area 130 mm * 130 mm

X-Y shrinkage 12.7% +/- 0.3%

Z shrinkage 15.0% +/- 0.5%

Density 3.1 g/cm^3

Dissipation factor 0.15%

Breakdown voltage >40,000 volts/mm

14

Table 2.2 shows Dupont 951 tape material’s thermal and mechanical properties

[22].

Table 2.2. Dupont 951 tape material thermal and mechanical properties [22].

Dupont 951

Tape

Thermal and mechanical

Properties

Conductivity 3.0 W/m.k

Young’s modulus 152 GPa

Fracture strength 320 MPa

Expansion coefficient 5.8 ppm/C

Specific heat 0.989 J/gC

Surface roughness <10 Micro-inches

Dupont 951 tape’s design parameters are shown in Table 2.3.

Table 2.3. Dupont 951 tape design parameters and considerations [23].

Conductors Preferred Advanced Minimum

Line width 150 um 30 um 100 um

Line to line spacing 150 um 30 um 100 um

Line to via pad spacing 150 um 30 um 100 um

Line to part edge spacing 500 um 250 um 250 um

Internal conductors Silver, Gold Silver, Gold Silver, Gold

External conductors Silver-Palladium,

Gold

Silver-Palladium,

Gold

Silver-Palladium,

Gold

VIAS

Diameter 250 um 100 um 150 um

Thermal via 250 um 250 um 250 um

15

Table 2.4 presents Dupont 951 tape’s considerations for passive devices [23].

Table 2.4. Dupont 951 tape design parameters and considerations for passive devices.

Capacitors

Dielectric thickness >16 um

Area <150 mm^2

Dielectric paste K=250, 500

Internal conductors Silver, Gold

External conductors Silver-Palladium, Gold

Precision 5-10%

Inductors

Conductors As per conductor spec.

Vias As per via spec.

Resistors

Length 750 um min.

Width 750 um min.

Resistance Tunable by aspect ratio

Sheet resistance 10, 100, 1000, 10000

Precision as fired 35%

Material Ruthenium oxide

Overlap 250 um min.

Several passive RF/microwave components can be constructed using a LTCC

process. A sample Spiral inductor with gold on Tape 951 from Dupont is shown

in Figure 2.6, and in Figure 2.7, we can see a dual port and single port, multi

finger and single capacitors with gold on Tape 951 from Dupont [24, 25].

16

Figure 2.6. Spiral inductor with gold on Tape 951 from Dupont [24].

Figure 2.7. Dual port and single port, multi finger and single capacitors with gold on Tape 951

from Dupont [25].

17

Figure 2.8 shows a sample of fabricated resistors on Tape 951 from Dupont [26].

Figure 2.8. Resistors on Tape 951 from Dupont [26].

DuPont offers two various tape compositions: 951 Green Tape and 943 Green

Tape. 951 Green Tape consists of high strength glass or a ceramic composite

which is suitable for applications below 20 GHz, and 943 Green Tape is a lead-

free glass ceramic composition and designed for applications up to 100 GHz. We

have applied 951 Green Tape systems of materials considering our frequency

range [22].

Ag and Au co-fired metallization are available for 951 Green tape systems, in

practice they use the combination of Ag for internal conductors and Au for

external conductors and wire bonding. In order to cut the cost, we applied Ag as

our conductors [27].

2.4 Transmission lines

Specific transmission line structures including coplanar wave guides, striplines

and microstrips have been considered greatly for characterizing materials [28, 29].

18

2.4.1 CBCPW

There are two main structures of coplanar lines, Coplanar Wave guides (CPW)

with no lower ground plane as illustrated in Figure 2.9 and Conductor-Backed

Coplanar Wave guides (CBCPW) with a lower ground plane known as CBCPW

as illustrated in Figure 2.10, [30,31].

S W S

t

H

W is the conductor width, S denotes the space between conductor and the ground

planes while H represents dielectric thickness and t is the conductor thickness.

S W S

t

H

A common approach to having an optimized CBCPWdesign is to consider the

limitations as

(2.4)

H>b W>b S=2a b=W+2S=246+2*100= 446 um H=100*6= 600 um.

Figure 2.9. Coplanar Waveguides (CPW) with no lower ground plane.

Figure 2.10. Conductor-Backed Coplanar Waveguides (CBCPW) with lower

ground plane.

19

To accurately predict the conductor-backed coplanar wave guides’ characteristic

impedance, we need to calculate the effective dielectric constant as

√

is the effective dielectric constant and K is the complete elliptic integral of

the first kind which can be calculated using MATLAB software as

(

)

where a is half of the spacing between the conductor and the ground planes and b

is W+2S as shown in (2.4), and we have

where is the relative dielectric constant of the substrate and K(k) is the

complete elliptic integral of the first kind which can be calculated using

MATLAB as

√

20

√

√

where

[ (

)]

[ (

)].

2.4.2 Stripline

The stripline calculations would be more specific when taking into consideration

the parallel plate assumptions and the large ground plane with zero thickness. To

accurately predict the stripline impedance, we must calculate the effective

dielectric constant [32].

Figure 2.11. Symmetric (balanced) stripline, case TD1 = TD2.

TD2

TCe

WCTD1

21

TC is the conductor’s thickness and WC represents the conductor’s width and is

the dielectric constant of the substrate. For the Symmetric (balanced) stripline

case, TD1 = TD2 the characteristic impedance of the system, Z0sym will be

(2.8)

where is the relative dielectric constant, this equation is valid when

WC/(TD1+TD2) < 0.35 and TC/(TD1+TD2) < 0.25.

For the offset (unbalanced) stripline Case, TD1 > TD2 we have

(2.9)

where TD1= 2A and TD2= 2B, [32].

2.4.3 Microstrip

The microstrip line calculations would be more specific when the parallel plate

assumptions and the large ground plane with zero thickness are taken into

consideration. To accurately predict the microstrip line impedance, we must

calculate the effective dielectric constant [33].

,)8.0(67.0

)(4ln

60 110

CC

DD

r

sym

TW

TTZ

e

,),,,2(),,,2(

),,,2(),,,2(2

00

000

rCCsymrCCsym

rCCsymrCCsymoffset

TWBZTWAZ

TWBZTWAZZ

ee

ee

22

Figure 2.12. Microstrip transmission line.

TC is the conductor’s thickness and WC represents conductor’s width and is the

dielectric constant of the substrate.

The characteristic impedance would be

(2.10)

This formula is valid when

0.1 < WC/TD < 2.0 and 1 < < 15

where

and F is

{

(

)

TD

TC

e

WC

.8.0

98.5ln

41.1

870

CC

D

r TW

TZ

e

,1217.012

12

1

2

1

DC

Cr

C

D

rre

TW

TF

W

T

e

eee

23

The first requirement to design a transmission line is to choose specific line

lengths in order to prevent the network analyzer from becoming ill-conditioned

[34].

Mr. Hoer defines two conditions for this purpose: first, the electrical length must

not be too near multiples of 180 and second, the physical length of a line whose

electrical length is less than 180° may be too short to be practical.

2.5 Measurement

2.5.1 Scattering Parameters

The scattering parameters describe the electrical behavior of linear electrical

networks when they are stimulated by electrical signals. Figure 2.13 shows a

device under the test’s transmitted, incident and reflected signals [35].

Figure 2.13. DUT transmitted, incident and reflected signals.

If the output is terminated to a perfect Z0 load, by measuring the magnitude and

the phase of incident, reflected and transmitted signals we can determine S11 and

Incident Transmitted

Reflected

IncidentTransmitted

Reflected

S21

S22

S12

S11

DUT

a1

b2

b1 a2

24

S21. This condition is equivalent to a2=0. S11 represents the input reflection

coefficient or the impedance of the DUT, while S21 is the forward transmisssion

coefficient [36].

If port 1 is terminated with a perfect load and we place the source at port 2 which

makes a1=0, S22 then S12 can be measured. S22 is the output reflection coefficient

or the output impedance of DUT and S12 is the reverse transmission coefficient as

in

(2.11)

2.5.2 The Vector Network Analyzer (VNA)

At high frequencies it is difficult to measure voltages and currents. On the other

hand, at high frequencies it is easy to measure the reflection and transmission of

electrical networks using network analyzers to measure the S–parameters [37].

A VNA combined with Cascade Microtech’s 50-ohm probes provides a powerful

tool for IC characterization, verification and measurement [38].

In order to make relevant measurements, the Network Analyzer has to be

calibrated for the desired range of frequency each time. The calibration process

.

01

01

02

02

2

112

2

222

1

221

1

111

a

a

a

a

a

bS

a

bS

a

bS

a

bS

25

means determining the systematic sources of errors which is implemented by

measuring known standards. Calibration removes mathematical errors from

subsequent measurements and shifts the reference planes of the measurements

[39].

26

Chapter 3

LTCC Dielectric Characterization

This chapter begins with a description of the selected test structures for LTCC

characterization at low and high frequencies. The parameters of the parallel plate

capacitors, CBCPWs, microstrips and striplines are discussed in details. The

calculations of the dielectric constant and loss tangent based on the Conformal

Mapping Technique will be discussed in Section 3.4. The next section will

introduce the test setup, which uses a 110 GHz VNA and a probe station for the

S-parameters measurements. In Section 3.5, the measurement data and ADS

simulated results will be compared. The de-embedding process of ports will be

described in Section 3.6 and the calculated dielectric constant and loss tangent

will be presented. Chapter 3 will conclude with a summarization in Section 3.7.

3.1 Introduction

For a low frequency range of 100 MHz to 1 GHz, the best technique to

characterize the LTCC would be using a parallel plate capacitor as described

previously in Chapter 2.2.6.

27

When designing these parallel plate capacitors, we need to consider the Dupont

951 LTCC design rules and parameters. For the characterization of the LTCC in a

higher frequency range of 1 GHz to 10 GHz, it requires employing Conductor-

Backed Coplanar Waveguides (CBCPW) with a lower ground plane, as described

previously in Chapter 2.2.6. CBCPWs have unique characteristics and

performance at high frequencies such as ready access to the ground plane, lower

dispersion, and less radiation loss compared to microstrips and striplines. In

addition, these types of transmission lines offer mechanical stability, thermal

dissipation capability, ease of fabrication and integration capability that are

attributed to the lower ground metallization. Using Agilent App CAD software,

we designed a set of different types of transmission lines with their LTCC design

rules in mind. To evaluate the expected measurement results, the designed

structures are simulated using an Agilent Design Systems (ADS) momentum

electromagnetic simulator. After fabricating the designed test structure, the

scattering parameters of our designed structures are measured using our in-house

VNA through a 50 ohm probe station. The next step would be calculating the

dielectric constant and loss tangent based on the “Conformal Mapping

Technique” using the measured scattering parameters.

3.2 Low Frequency Characterization (100 MHz to 1

GHz)

The capacitance can be easily calculated if the geometry of the conductors and the

dielectric properties of the insulator between the conductors are known [40]. For

28

example, the capacitance of a parallel-plate capacitor made of two parallel plates,

both with an area of A separated by a distance d is approximately equal to

where “κ” is the is the dielectric constant of the material, ε0 ≈ 8.85 x 10-12 F/m

which is the free space permittivity, and C is the capacitance. Knowing the

dimensions of a parallel plate capacitor, the dielectric constant of the insulator

material can be easily calculated as a function of its measured capacitance using

Figure 3.1. Ideal parallel plate capacitor, A is the area of the plates, and d is the plate separation.

We have designed five parallel plate capacitors for a frequency range of 100 MHz

to 1GHz, according to the design rules summarized in Table 3.1, [41].

29

c

a b

Table 3.1. Design Guidelines for LTCC according to Hirai [41].

Item Std.

a Capacitor Size [mm] ~5.0

b Spacing [mm] >a

c Distance among each layers [um] ~40

Using Agilent Advanced Design System software, we obtained the scattering

parameters of our capacitors, assuming “κ” of 7.99 for the preliminary simulation

of the LTCC parallel-plate capacitors. The simulated scattering parameters that

are used to predict the measurement data base after de-embedding will eventually

be used to determine the dielectric constant and loss tangent of the LTCC

substrate from 100MHz to 1 GHz.

30

Figure 3.2. Three dimensional visualization of our designed capacitors in Agilent Advanced

Design System.

Figure 3.3. Scattering parameters of a capacitor with A=7*7 mm^2, and d=100 um, “κ” =7.99, T=6

um, σ=6.3*e+07 S/m.

3.3 High Frequency Characterization (1GHz to 10 GHz)

Conductor-Backed Coplanar Waveguides (CBCPW) with lower ground planes are

widely used in Microwave Integrated Circuits (MICs) and Monolithic Microwave

Integrated Circuits (MMICs). CBCPWs have demonstrated to be the most

appropriate candidates for LTCC characterization due to their characteristics and

performance at higher frequencies. In addition to having ready access to the

ground plane, mechanical stability, thermal dissipation capability, and ease of

fabrication and integration capability, CBCPWs offer lower dispersion and less

31

radiation loss compared to microstrip lines and striplines. Taking into account

some dimensional restrictions, several coplanar transmission lines with different

dimensions were designed as listed in Table 3.3. As can be seen in Figure 3.4,

fourteen sets of coplanar wave guides, ten micro striplines and twelve sandwich

striplines were designed; they were simulated using the Agilent Design Systems

Momentum Electromagnetic Simulator and are listed in Table 3.2 for comparison.

For preliminary simulations, a dielectric constant value of 7.99 was assumed for

the LTCC substrate. Silver was used as the conductor with an electrical

conductivity value of 6.3*10^7 S/m, while the conductor’s thickness, T, is 6 µm.

The width of the conductor, W, is designed such that the transmission line is

matched to 50 ohm. We used six layers of LTCC substrates each with 100 um

width, which gives the height of the substrate as H=6*100=600 um.

L is the length of our test structures which is a multiple of λ/4.

Table 3.2. Design parameters of the CPWs, microstrips and striplines.

CPW Microstrip Stripline

L

mm

S

µm

T

µm

H

µm

W

µm

L

mm

T

µm

H

µm

W

µm

L

mm

T

µm

H

µm

W

µm

1.150 100 6 600 258 2.65 12 600 761 2.65 6 600 151

2.65 100 6 600 258 3 12 600 761 2.65 6 600 151

5.150 100 6 600 258 7.115 12 600 761 3 6 600 151

10.150 100 6 600 258 26.5 12 600 761 7.115 6 600 151

26.5 100 6 600 258 71.15 12 600 761 26.5 6 600 151

81.6 100 6 600 258 95 12 600 761 95 6 600 151

32

Figure 3.4. Layouts of test structures including the transmission lines and capacitors.

After fabricating the designed test structures, the scattering parameters of our

designed structures were measured using a 50 ohm probe station VNA from 100

MHz to 10 GHz. Ultimately, the LTCC dielectric characteristics such as the

characteristic impedance, attenuation constant, effective dielectric constant and

loss tangent will be calculated based on the Conformal Mapping Technique

Calculations using the measured scattering parameters [42].

33

3.3.1 CBCPW Electromagnetics Simulation

The CBCPW formulas will be disscussed in details in Section 3.4.1. A 50 ohm,

10150 µm CBCPW is shown in Figure 3.5. We utilized ADS EM simulator to

obtain the scattering parameters, and the smith chart shown in Figure 3.6 which

confirm the 50 ohm matching from dc to 10 GHz frequency range.

Figure 3.5. Designed 50 ohm sample CBCPW with W=246 µm, l=10150 µm, G=100 µm, we have

considered the Dupont 951 technology: T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99.

34

Figure 3.6. Scattering parameters and smith chart of CBCPW.

3.3.2 Stripline Electromagnetics Simulation

The formulas for the stripline were discussed in detail in Section 2.4.2. Figure 3.7

shows a 50 ohm, 10150 µm stripline that was designed using App CAD software.

ADS EM simulator was utilized to obtain the scattering parameters and the smith

chart shown in Figure 3.8 which confirm the 50 ohm matching from dc to 10

GHz frequency range.

Figure 3.7. Designed 50 ohm sample stripline with W=151 µm, l=10150 µm, we have considered

the supplier technology: T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99.

freq (100.0MHz to 10.00GHz)

S11

35

Figure 3.8. Scattering parameters of stripline.

3.3.3 Microstrip Electromagnetics Simulation

The microstrip forumlas for this simulation was already discussed in detail in

Section 2.4.3. Figure 3.9 shows a 50 ohm, 1150 µm stripline that was designed

using App CAD software. The scattering parameters and the smith chart shown in

Figure 3.10 were obtained from ADS EM simulations which confirm the 50 ohm

matching from dc to 10 GHz frequency range.

Figure 3.9. Designed 50 ohm sample microstrip with W=761 µm, l=1150 µm, we have considered

the supplier technology: T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99.

36

Figure 3.10. Scattering parameters and smith chart of microstrip.

From the simulated scattering parameters of the CBCPW sample, stripline and

microstripline shown in Figure 3.5 through Figure 3.10, it is confirmed that they

offer 50 ohm matching over the entire frequency band of 1GHz to 10 GHz. Table

3.3 summerizes the design parameters of the final fourteen CBCPWs. W is the

signal line width, S defines the seperation space between the signal and the

ground lines, Wg is the ground line width, H is the width of the six layer LTCC

substrate, t denotes the conductor’s thickness dictated by the Dupont 951 design

rules and L is CBCPW lengths designed according to [24].

37

Table 3.3. Design parameters of CBCPWs with ground plane.

38

3.4 Dielectric Constant and Loss Tangent Calculations

3.4.1 Dielectric Constant

The dielectric constant ( is the ratio of the permittivity of a substance

( ) to the permittivity of free space ( . The dielectric constant is a bulk

material property, while the effective dielectric constant is a parameter that

depends on the transmission line geometry.

The propagation constants of a CBCPW can be related to the measured S21 by

, (3.3)

where, α denotes the attenuation constant in decibel per centimeter (dB/cm), β is

the phase constant in cm-1 and ΔΦS21 is the phase shift of the transmission

coefficient S21 ,while l is the transmission line length in centimeters. ΔΦS21 is

related to the effective dielectric constant εeff by

√

. (3.4)

From the effective dielectric constant values, the relative dielectric constant of the

LTCC dielectric material and the characteristic impedance of the lines are

extracted using analytical expressions based on the quasi-TEM approach [43].

39

The approximate Conformal Mapping Technique [28] gives the effective

dielectric constant as

and characteristic impedance as

√

, (3.6)

where K is the complete elliptic integral of the first kind [43], and K’ is its

complementary function,

√

√

and

√ ,

for 0<k<0.7070 and 0<K/K’<1

√

√

40

√

√

where,εr is the dielectric constant of the LTCC film, H is the film’s thickness, S

denotes the spacing to the adjacent ground, and W is the trace width. Htotal=600

µm, W=240 µm, and S=100 µm.

We utilized MATLAB for solving the elliptic functions.

3.4.2 Loss Tangent

The CPW transmission line can also be described in terms of its distributed

resistance, inductance, capacitance and conductance (R, L, C, G), given by

, (3.7)

where C and G are given by the relations

[

]

[

]

where

41

3.5 Measurement

After fabricating the designed test structures, the scattering parameters were

measured using a 110 GHz Vector Network Analyzer with a 50 ohm probe station

in a Microwave to Millimeter Wave Laboratory located at the Electrical and

Computer Engineering Research Facility (ECERF) at the University of Alberta as

shown in Figure 3.11.

Figure 3.11. VNA probe station at M2M.

42

.

3.5.1 Measurement versus Simulation

Figure 3.12 shows the test structures fabricated by ACAMP on Dupont 951

LTCC.

Figure 3.12. Test structures fabricated by ACAMP on Dupont 951 LTCC.

43

Figure 3.13. 50 ohm miniature Z probe pitch of the VNA.

Figure 3.14. Input port of a stripline to be measured under VNA’s microscope.

Figure 3.14 shows the input port of one of the striplines to be measured using a 50

ohm probe station under a VNA’s microscope.

To ensure the proper testing of our test structures in the required frequency range ,

the measured scattering parameters of the test structures were imported to an ADS

EM simulator through the “S2P” instance file. A comparision of the measured

results and the scattering parameters from the ADS EM simulations were done for

our model verification as demonstrated in Figure 3.15.

44

Figure 3.15. ADS file to compare measurement results and Electromagnetic simulation data.

Figure 3.16 through Figure 3.27 show the ADS EM simulation results of the

scattering parameters’ phase and amplitude in degree and decibel for 650 µm,

1150 µm, 5150 µm and 10150 µm CBCPW lines. The measured scattering

parameters of the mentioned transmission lines are illustrated on the charts for

comparison purposes.

45

Figure 3.16. Measured and simulated scattering parameters of the 650 µm CBCPW.

Figure 3.17. Measured and simulated ΔΦS21 of the 650 µm CBCPW.

5 10 15 20 25 30 350 40

-60

-50

-40

-30

-20

-10

-70

0

freq, GHz

S Pa

ram

eter

s (d

B)

Measurement Vs. Simulation

-----Simulation

Measurement

-----Simulation

Measurement

46

Figure 3.18. Measured and simulated S21 magnitude of the 650 µm CBCPW.

Figure 3.19. Measured and simulated scattering parameters of the 1150 µm CBCPW.

5 10 15 20 25 30 350 40

-50

-40

-30

-20

-10

-60

0

freq, GHz

S Pa

ram

eter

s (d

B)

Measurement Vs. Simulation

-----Simulation

Measurement

-----Simulation

Measurement

47

Figure 3.20. Measured and simulated ΔΦS21 of the 1150 µm CBCPW.

Figure 3.21. Measured and simulated S21 magnitude of the 1150 µm CBCPW.

-----Simulation

Measurement

-----Simulation

Measurement

48

Figure 3.22. Measured and simulated scattering parameters of the 5150 µm CBCPW.

Figure 3.23. Measured and simulated ΔΦS21 of the 5150 µm CBCPW.

5 10 15 20 25 30 350 40

-60

-50

-40

-30

-20

-10

-70

0

freq, GHz

S Pa

ram

eter

s (d

B)

Measurement Vs. Simulation

-----Simulation

Measurement

-----Simulation

Measurement

49

Figure 3.24. Measured and simulated ΔΦS21 of the 5150 µm CBCPW.

Figure 3.25. Measured and simulated scattering parameters of the 10150 µm CBCPW.

-----Simulation

Measurement

-----Simulation

Measurement

50

Figure 3.26. Measured and simulated ΔΦS21 of the 10150 µm CBCPW.

Figure 3.27. Measured and simulated S21 magnitude of the 10150 µm CBCPW.

As shown from Figures 3.16 through 3.27, the difference between the measured

and simulated results confirm the nessecity of de-embedding the transmission

lines, which will be described in the following section.

-----Simulation

Measurement

-----Simulation

Measurement

51

3.6 De-embedding DUT

An accurate characterization of the surface mount Device Under Test (DUT)

requires the test fixture characteristics to be removed from the measured results

which includes the effects of the coaxial interfaces, the VNA and the ports of the

transmission lines [44].

Fixture A DUT Fixture B

FA21 S21 FB21

FA11 FA22 S11 S22 FB11 FB22

FA12 S12 FB12

If we consider the test fixture and DUT as three cascaded networks and use the T-

parameter matrix, we can conclude

The resulted matrix represents the T-parameters of the test fixture and the DUT

measured by the VNA. Our goal is to de-embed the two sides of the fixture, TA

and TB, and gather the information from the DUT. So we should multiply each

side of the measured results by the inverse T parameter matrix of the fixture

which yields to the T-parameter of the DUT itself

Figure 3.28. Signal flow graph representing the test fixture halves and the Device Under

Test (DUT) [44].

52

The T-parameter matrix can then be converted back to the desired S-parameter

matrix [45] using

S11=T21/T11 S12= (T11T22-T12T21)/T11 (3.10)

S21=1/T11 S22=-T12/T11.

To remove the test fixture characteristics from the transmission lines, we have to

de-embed the effects of the ports. For de-embedding purposes we have designed

dummy ports exclusively for each test structure so that we can measure their

scattering parameters and de-embed them from the transmission lines’ scattering

parameter measurements. Since our dummy ports are designed as one port, we

need to write a MATLAB code to convert the one port dummy T parameters to its

equivalent two-port dummy T parameters.

Using the formulas above, we are able to de-embed the test fixture effects and

calculate the dielectric properties of the LTCC substrate precisely.

In the following section we will describe how to model the ports properly.

3.6.1 Modeling Port as a RLC Network

Intially, we modeled the ports of our designed test structures with a parrallel

capacitor to the ground. This model was not accurate enough to demonstrate

reasonable results. Measuring the real part of the port impedance as shown in

Figure 3.29 confirmed the existance of a resistive part in the port, consequently

we modeled the transmission line port as a RLC circuit as shown in Figure 3.30.

53

Figure 3.29. Measured real part of the port impedance.

Figure 3.30 shows the RLC model for the transmission line’s ports, where Z1=R,

Z2= jwL and Z3= 1/jwC [49]. If we write the ABCD-Parameters of the circuit in

Figure 3.30, we will have

A=1+Z1/Z3 B=Z1+Z2+Z1Z2/Z3 (3.11)

C=1/Z3 D=1+Z2/Z3 .

Then we will convert the ABCD-Parameters to S-Parameters [50] using

S11=(A+B/Z0-CZ0-D)/(A+B/Z0+CZ0+D)

S12=(2(AD-BC))/ (A+B/Z0+CZ0+D)

Z2 Z1

Z3

Figure 3.30. RLC model for the transmission line’s ports [46].

54

S21=2/(A+B/Z0+CZ0+D)

S22=(-A+B/Z0-CZ0+D)/(A+B/Z0+CZ0+D). (3.12)

Ultimately, when we convert the S-parameters to the T-parameters it will lead to

T11=1/S21 T12=-S22/S21 (3.13)

T21=S11/S21 T22= (S12S21-S11S22)/S21 .

Now we can use the de-embedding formulas described in Section 3.6 and extract

the T-parameters of our DUT. Converting the T-parameters back to S-parameters

will give us the de-embedded measurement results of our test structures. Now we

can utilize the Conformal Mapping Technique [46] described in Section 3.4 to

characterize the LTCC and calculate the dielectric constant and loss tangent.

3.6.2 Simulation Results

In this section, to verify the necessity of de-embedding the effect of the ports, we

will compare the measured and simulated results of the test structures before and

after de-embedding. Figures 3.31 shows the dielectric constant of LTCC based on

ADS EM simulations,while Figure 3.32 and 3.33 illustrate the dielectric

properties of the LTCC based on the measurement results up to 10 GHz before

de-embedding the test fixture from our test structures. As shown, there is a

signifinacnt discrepenacy between the dielectric constant and the loss tangent of

two structures.

55

Figure 3.34 and 3.35 show the calculated dielectric constant and loss tangent of

the LTCC based on the comformal mapping tecnique using the de-embedded

scattering parameter measurement results of the CBCPWs. The de-embedded

results confirm that the measuremnt and simulation results follow each other

closely.

Figure 3.31. Dielectric constant of the LTCC using the ADS simulation results up to 40 GHz.

56

Figure 3.32. Dielectric constant of the LTCC using the measurement results before de-embedding

up to 10 GHz.

Figure 3.33. Loss tangent of the LTCC using the measurement results before de-embedding up to

10 GHz.

57

Figure 3.34. Dielectric constant of the LTCC using the measurement results after de-embedding

up to 10 GHz.

Figure 3.35. Loss tangent of the LTCC using the measurement results after de-embedding up to 10

GHz.

58

Finally, after de-embedding the CBCPW ports, the dielectric constant and loss

tangent are calculated using the method described in this chapter. Table 3.4

denotes the dielectric properties of the LTCC at eleven discrete frequencies.

Table 3.4. Loss tangent and dielectric constant of LTCC.

Frequency

GHz

Dielectric

Constant

Loss

Tangent

0.5 8 0.1

1 7.8 0.02

2 7.6 0.01

3 7.5 0.06

4 7.4 0.05

5 7.3 0.01

6 7.3 0.04

7 7.3 0.01

8 7.3 0.02

9 7.3 0.02

10 7.3 0.01

3.7 Summary

In Chapter 3 we designed five parallel plate capacitors and fourteen CBCPWs

using Agilent App CAD and ADS EM simulations to characterize the Dupont 951

LTCC substrate from 100 MHZ to 10 GHz. To obtain the scattering parameters of

the CBCPW test structures, the effects of the pads are de-embedded from the

59

measured scattering parameters using a conventional de-embedding method. In

order to de-embed the test fixture we needed to model the ports of our test

structure designs as two port RLC circuits using MATLAB software. Finally the

dielectric constant and loss tangent were calculated accurately, utilizing the

Conformal Mapping Technique.

60

Chapter 4

Proposed De-Embedding Method

In this chapter, we will present a new de-embedding method for removing the

effect of the test fixtures, such as the pads, on the scattering parameters of the

device under test. The proposed method not only de-embeds the pad but also

certain lengths of the transmission line connecting the pads to the device under

test leaving the electromagnetic field around de-embedded structure relatively

unchanged from that of the original structure. This will produce more accurate

measurement results for a de-embedded structure, and consequently a more

accurate characterization of the material.

Section 4.1 introduces the proposed de-embedding method. Then, we will develop

the theory of the method in Section 4.2. The properties of reciprocal and non-

reciprocal networks will be studied in 4.3 to facilitate the calculation of the

scattering parameters of the de-embedded structure.

In Section 4.4, we will compare the electromagnetic fields of the de-embedded

test structure and the original test structure to prove the improvement in the

proposed method compared to the conventional de-embedding methods. Finally,

61

the numerical results for the dielectric constant and loss tangent of the LTCC

material obtained based on the proposed de-embedding technique will be

illustrated in Section 4.5. Chapter 4 is summarized and concluded in Section 4.6.

4.1 Introduction

It is necessary to de-embed the effect of the test fixtures such as the pads on the

DUT’s measured scattering parameters to obtain its own scattering parmameters.

In the convetional de-embedding method, the scattering paramaters of the pads

are removed by measuring the single-port scattering parmaters of the dummy pads

that are implemented and tested along with the device under test. The input pad,

the de-embedded DUTand the output are considered to be three cascaded blocks,

this means the overall transmission parmaters of the non-embedded structure can

be written as

padoutputDUTembeddeddepadinputoverall TTTT ___ . (4.1)

and the scattering parameters of the de-embedded DUT can be obtained by

1

_

1

__

padoutputoverallpadinputDUTembeddedde TTTT . (4.2)

This method assumes that the electromganetic enviroment arount the de-

embedded DUT is the same as the overall DUT including the pads. However, in

many cases, the size of the pads is in the same scale as the DUT and their effects

on the electrogmanetic fields in the vicinity of the DUT can not be negelected.

62

Therefore, the resulting scattering parmaters based on the above equation does not

accurately represent the scattering parameters of the DUT if we were able to test it

without pads.

In order to obtain accurate results related only to the de-embedded DUT, we

propose that part of test structure and the pads be de-embedded from the

measurement results, instead of only removing the effect of the pads. This will

leave some distance between the pad and the actual DUT, thus mininizing the

effect of the pads on the electromganetic fields around the DUT. Of course, this

method requires that the part of test structure and the pads be constructed as a

dummy test fixture along with the device under test. Illustrated in Figure 4.1, the

middle DUT represents the de-embedded transmission line using the conventional

methods while the lower DUT demonstrates the de-embedded transmission line

using the proposed de-embedding method.

Figure 4.1. Conventionally de-embedded transmition line in the middle and the proposed de-

embedded line at the bottom.

63

4.2 Theory of Proposed De-embedding Method

In this section, we will apply the proposed de-embeeding method to our dielectric

charatrization applications.We have selected the designed 5000 µm CBCPW as

our main test structure to be measured to extract the dielectric constant and loss

tangent of the LTCC substrate. Using our RF probes that have a 100 µm pitch,

the designed CBCPW lines are connected to the the specially designed input and

output ports in order to be able to measure the s-parameters of the 5000 µm

CBCPW lines. This set up is shown in Figure 4.2.

Figure 4.2. 5150 µm CPW transmission line including input and output ports, W=246 µm, l=5150

µm, G=100 µm, T=6 µm, H=6*100 µm, σ=6.3*e+07 S/m and “κ”=7.99.

However, the designed port will change the electrogmanetic field in the vicinity

of the 5000 µm CBCPW, leading to inaccurate results if the structure is tested this

way. Therefore, in order to minimize the effect of port on the electromagnetic

field around the 5000µm CBCPW, we have added two 2575µm CBCPW sections

64

with exactly similar structures as the original 5000µm CBCPW line to both ends

of the DUT. Then, we fabricated and measured the scattering parmaters of a

10150µm CBCPW line to be used for accurate charaterization of a 5000 µm

CBCPW line. In addition, we needed to fabricate our test fixture, a 2575 µm

CBCPW line connected to the port, and measure its scattering parameters making

it possible to de-embed their effect on the scattering parmaters. In order to

meausre the two-port scattering parameters, we constructed two back-to-back

2575 µm structures to form a 5150 µm CBCPW with input and output ports.

4.3 Electromagnetic Field Comparison

In Section 4.3, we will confirm that in order to obtain accurate results related only

to the de-embedded DUT, parts of test structure in addition to the pads should be

de-embedded from the measurement results. This will leave some distance

between the pads and the actual DUT, minimizing the effect of pads on the

electromagnetic fields around the DUT.

We will compare the similarities and discrepancies of the electromagnetic field

distributions of a CPW in the vicinity of pads and in some distance from the pads.

We can visualize the electric field and the magnetic field of CPWs using ADS

FEM simulator.

Figure 4.3 shows CPW Electric-E and Magnetic-H field distributions in theory;

the solid lines show electric field of the CPW while the dashed lines demonstrate

its magnetic field.

65

Figure 4.3. CPW Electric-E and Magnetic-H field distribution.

Figure 4.4.a shows the electric field distribution of a short CBCPW with physical

ports and Figure 4.4.b visualizes its magnetic field distribution using an ADS

FEM simulator. As can be seen, there is a significant discrepancy in the

electromagnetic fields in the vicinity of the physical ports of the CBCPW, this

will result in less accurate calculations of the material characterization if we de-

embed the DUT conventionally.

Figure 4.5.a shows the electric field distribution of the 10150 µm CBCPW with

physical ports and Figure 4.5.b visualizes its magnetic field distribution using an

ADS FEM simulator. If we de-embed some parts of the transmission line in

addition to the ports as described in details earlier, we will have much more

similar electromagnetic fields to the original line. This will produce more accurate

measurement results for a de-embedded structure, and consequently a more

accurate characterization of the LTCC material.

66

The red color in Figure 4.4 and 4.5 represents the regions with maximum voltage

while the green color visualizes the regions bearing the average voltage and the

blue regions have zero voltage.

(a)

(b)

Figure 4.4. (a) Electric field distribution of a 650 µm CBCPW, (b) Magnetic field distribution of a

650 µm CBCPW.

67

(a)

(b)

Figure 4.5. (a) Electric field distribution of 10150 CBCPW, (b) Magnetic field distribution of

10150 CBCPW.

4.4 Characterization of Test Fixtures

After fabricating the designed 5150 µm CBCPW structure, we measured its

scattering parameters using a 110 GHz VNA through a 50 Ohm probe station.

The results were used to obtain the scattering parameters of our test fixture, a

2575 µm CBCPW connected to a port, as described below.Using (4.3), we first

converted the amplitude and phase of the 5150 µm transmision line’s S11, S12, S21

68

and S22 parameters from degrees and decibles to real and imaginary numbers as it

will be required later,

Sij = (10^(Sij5150./20))*(i.*sin(Sij5150p.*pi/180)+cos(Sij5150p.*pi/180)) (4.3)

where Sij5150 is the measured amplitude of the scattering parameter of the 5150

µm transmision line in dB, and Sij5150p is the measured phase of its scattering

parameter in degree.

If we consider the 5150 µm CBCPW structure including its two port as a cascade

of two 2575 µm CBCPW lines, each with one port, we can write the following

relation for the overall transmission parameters (T parameters ) of the 5150 µm

line as

TA1.TA2=T5150 (4.4)

where TA1 and TA2 are the T parameters of each half of the 5150 µm line

including the input and output ports. If we calculate TA1 and TA2 we can obtain the

scattering parameters of a 2575 µm line including the dummy ports by converting

its T parameters to S parameters. In order to do so, we first write the T parameters

of the two test fixtures as a function of their S parameters in Equation 4.4

resulting in the following four equations to be solved simultaneously,

(S12A1* S21A1 - S11A1* S22A1)* (S12A2* S21A2 - S11A2* S22A2)/ (S21A1* S12A2) - S11A1*

S11A2/ (S21A1* S12A2) = (S125* S215 - S115* S225)/ S125

(S12A1* S21A1 - S11A1* S22A1)*S22A2/ (S21A1* S12A2) + S11A1/ (S21A1* S12A2) = S115/

S215

69

S22A1* (S12A2* S21A2 - S11A2* S22A2) / (S21A1* S12A2) + S11A1/ (S21A2* S12A2) = S225/

S215

- S22A1^2 / (S21A1* S12A2) + 1/ (S21A1* S12A2) = 1/ S215 . (4.5)

Since the two test fixtures are exactly the same except that the input and output

are swapped, we can conclude that their S parameters are identical if we change

their input port and output port in the matrix,

. (4.6)

Using the above equalities, we can simplify the four equations to

(S12A* S21A - S11A* S22A)^2/ (S21A* S12A) - S11A^2/ (S21A* S12A) = (S125* S215 -

S115* S225)/ S125

(S12A* S21A - S11A* S22A)*S22A/ (S21A* S12A) + S11A/ (S21A* S12A) = S115/ S215

S22A* (S12A* S21A - S11A* S22A) / (S21A* S12A) + S11A/ (S21A* S12A) = S225/ S215

- S22A^2 / (S21A* S12A) + 1/ (S21A* S12A) = 1/ S215 . (4.7)

70

In order to further simplify the above equations, we need to review the properties

of the reciprocal networks. In a reciprocal network, the power losses are equal

between any two ports regardless of the direction of propagation, that is S21=S12

for a two-port network. If a network is passive and contains

only isotropic materials, we can categorize it as a reciprocal network. For

instance, cables, attenuators, and all passive power splitters and couplers are

reciprocal networks [51].

On the other hand we have non-reciprocal networks in which the scattering

parameter S21 is much different from S12. Obviously non-reciprocal networks

contain anisotropic materials such as the class of materials known as ferrites, from

which circulators and isolators are made. In anisotropic materials, depending on

which direction a signal propagates, the electrical properties such as the relative

dielectric constant would be different [51]. We categorized the RF amplifiers and

isolators as non-reciprocal networks, because the scattering parameter S21 is very

different from S12.

Since our network is passive and contains only isotropic materials, we have a

reciprocal network, which means S21A=S12A and S215=S125.

Thus we can simplify the previous sets of equations in (4.7) to the equations in

(4.8). Matematica software is utilized to solve the above equations which

ultimately results in the scattering parameters of a 2575 µm line including the

dummy ports,

(S12A^2 - S11A* S22A)^2/ S12A^2 - S11A^2/ S12A^2 = (S125^2 - S115^2)/ S125

71

(S12A^2 - c* S22A)*S22A/ S12A^2 + S11A/ S12A^2 = S115/ S125

- S22A^2 / S12A^2 + 1/ S12A^2 = 1/ S125 . (4.8)

Having calculated the T parameters of the test fixtures, the final step would be to

calculate the T parameters of the DUT of the 5000 µm CBCPW line using

TA1.T5000.TA2=T10150 , (4.9)

where, TA1 and TA2 are the T parameter matrix of the 2575 µm transmission lines

and their dummy ports which were calculated previously. Converting the

measured S-parameters of the 10150 um CBCPW line to the T-parameters, we

can compute the T-parameters of the 5000 um CBCPW line using

1

210150

1

15000

AA TTTT. (4.10)

Equation 4.10 produces the scattering parameters of the de-embedded 5000 µm

CBCPW based on the proposed de-embedding method.

4.5 Dielectric Characterization Results

Using the Conformal Mapping Technique described in Chapter 3 enables us to

calculate the dielectric properties of the LTCC based on the new de-embedding

method. The results are more accurate, since the electromagnetic field of the de-

embedded line with the proposed technique is much more similar to the original

line than the conventionally de-embedded lines. Figure 4.6 shows the loss tangent

of the Dupont 951 LTCC utilizing the measurement results after de-embedding up

to 10 GHz using our proposed technique.

72

Figure 4.6. Loss tangent of Dupont 951 LTCC using measurement results after de-embedding up

to 10 GHz using our proposed analytical method.

Table 4.1 represents the improved loss tangent of the LTCC which verifies the

superior performance of our proposed de-embedding analytical technique.

Table 4.1. Improved loss tangent of Dupont 951 LTCC.

Frequency

GHz

Loss

Tangent

0.5 0.01

1 0.01

2 0.01

3 0.01

4 0.007

5 0.009

6 0.006

7 0.01

8 0.008

9 0.009

10 0.01

73

4.6 Modeling of Other LTCC Devices

For modeling LTCC devices such as transmission lines, capacitors, inductors and

other passive elements, one can easily take advantage of the available Agilent

models and simply replace the loss tangent and dielectric constant of the Dupont

951 LTCC reported in Table 4.1.

Figure 4.7 shows a sample stripline and its substrate characteristics. In Figure 4.8

we demonstrated that the substrate properties can be defined according to the loss

tangent and dielectric constant reported in Table 3.4 and Table 4.1 at the desired

frequencies.

Figure 4.7. Model of stripline in ADS assuming Dupont 951 LTCC as its substrate.

74

Figure 4.8. Creation of the substrate of Dupont 951 LTCC for a stripline in ADS.

However, there have been considerations in the LTCC design kits in contrary to

the design kits developed for MMIC’s and RFIC’s [50].

There are no industry standards for a LTCC design kit, but there are many other

variables such as dielectric, metallization, resistance layers, and geometry, via

size and placement of the cavities. As mentioned earlier there are different

numbers of layers in the LTCC, as well as in embedded RF components and

integrated active devices which may be on any layer.

The Ansoft designer has some features for LTCC such as fully parameterizable

geometry and arbitrary two dimensional and three dimensional vias. There are

75

variable stack-up properties such as the thickness or height of the material or

conductor, and the dielectric constant of the material and the conductivity of the

metal [51].

4.7 Summary

In Chapter 4 we presented a novel de-embedding technique that removes the

effects of test fixtures such as ports more accurately compared to the convention

de-embedding methods.

In fact, the proposed method not only de-embedded the pad, but also certain

lengths of the transmission line connecting the pads to the device under test

leaving the electromagnetic field around de-embedded structure relatively

unchanged from that of the original structure. This produced more accurate

measurement results for the de-embedded structure. Based on the proposed

method, we characterized the LTCC dielectric material with more accurate results

for the loss tangent of the material compared to the previously calculated

parameters based on the conventional method, and consequently more accurate

characterization of the LTCC material.

76

Chapter 5

Conclusions

The focus of this dissertation was on the characterization of Low Temperature

Co-fired Ceramic (LTCC) for microwave and Radio Frequency (RF) applications.

In this work, the LTCC dielectric parameters were characterized from 100 MHz

to 10 GHz. To estimate the dielectric constant and loss tangent of a LTCC

substrate, several test structures were fabricated on LTCC substrates and their S-

parameters were measured using a VNA. We investigated various measurement

techniques which led us to choose a parallel plate capacitor for the

characterization of a LTCC substrate from 100 MHz to 1 GHz and a Conductor

Backed Co Planar Waveguide (CBCPW) from 1 GHz to 10 GHz.

In Chapter 3 we designed five parallel plate capacitors and fourteen CBCPWs

using Agilent App CAD and ADS EM simulations to characterize the Dupont 951

LTCC substrate from 100 MHZ to 10 GHz. To obtain the scattering parameters of

the CBCPW test structures, the effects of the pads were de-embedded from the

measured scattering parameters using a conventional de-embedding method. In

order to de-embed the test fixture we needed to model the ports of our test

structure designs as two port RLC circuits using MATLAB software. Finally, the

77

dielectric constant and loss tangent were calculated accurately, utilizing the

Conformal Mapping Technique.

In Chapter 4 we presented a novel de-embedding technique to de-embed the 5150

µm CBCPW test structure taking advantage of the measurement results of the

10150 µm transmission line. Having the knowledge that we have a reciprocal

network, some simplifications were applied to the equations and applying

Matematica software solved the equations and saved us a lot of time.

We also computed the specified lines’ electromagnetic field distribution using

ADS FEM simulations which confirmed the similarity of the transmission lines’

electromagnetic fields when they are de-embedded using our analytical technique.

The proposed method not only de-embedded the pad, but also certain lengths of

transmission line connecting the pads to the device under test leaving the

electromagnetic field around de-embedded structure relatively unchanged from

that of original structure. This produced more accurate measurement results for

the de-embedded structure, and consequently a more accurate characterization of

LTCC material.

78

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